[CERC2013] Bus

题面翻译

有一个公交车，初始时车上有 $n$ 个人，每停一站，车上会先下去一个人，然后再下去车上剩下的人数的一半的人。已知经过了 $k$ 个站之后，车上没人了。现在，给出 $k$，求一开始车上的人数 $n$。

$1⩽k⩽30$。

Translated by Eason_AC
2020.11.12

题目描述

A bus with $n$ passengers opens its door at the bus stop. Exactly half of its passengers and an additional half of a passenger get out. On the next stop, again, half of the passengers plus half of a passenger leave the bus. This goes on for $k$ stops in total. Knowing that the bus leaves the last stop empty, and that no one was hurt during the trip, determine the initial number $n$ of people in the bus.

输入格式

The first line of input contains the number of test cases $T$. The descriptions of the test cases follow:

The only line of each test case contains the number of stops $k$, $1\le k\le 30$.

输出格式

For each test case, output a single line containing a single integer—the initial number of bus passengers.

样例 #1

样例输入 #1

2
1
3
1
2
3

样例输出 #1

1
7
1
2

提示

Time limit: 1000 ms, Memory limit: 1048576 kB.

Central Europe Regional Contest (CERC) 2013

分析：

因为每次到一个站都会先下1个人，在下下去车上剩下的人数的一半的人，所以我们可以直接倒推~~

代码：

#include

using namespace std;

int T;

int k;

int n;

int main()
{
    cin>>T;
    
    while(T--)
    {
        n=0;//将n清0
        
        cin>>k;
        
        for(int i=1;i<=k;i++) 
        {
			n*=2;//将下车后剩下的人数乘2
			
			n++;//再将n+1
        }
        
        cout<<n<<endl;//输出n
    }
    
    return 0;
}
1
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7
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9
10
11
12
13
14
15
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17
18
19
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21
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29
30
31
32

结束啦~~~